Week 4 Confidence Intervals and Chi Square  (Chs 11 – 12)   Let’s look at some other factors that might influence pay.       <Note: use right click on row numbers to insert rows to perform analysis below any question> For question 3 below, be sure to list the null and alternate hypothesis statements.  Use .05 for your significance level in making your decisions.           For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculations you performed.                                       1 One question we might have is if the distribution of  graduate and undergraduate degrees independent of the grade the employee?               (Note: this is the same as asking if the degrees are distributed the same way.)             Based on the analysis of our sample data (shown below), what is your answer?             Ho: The populaton correlation between grade and degree is 0.                 Ha: The population correlation between grade and degree is > 0               Perform analysis:                       OBSERVED A  B C D E F Total             COUNT – M or 0 7 5 3 2 5 3 25              COUNT – F or 1 8 2 2 3 7 3 25             total 15 7 5 5 12 6 50             EXPECTED                             7.5 3.5 2.5 2.5 6 3 25   <Highlighting each cell with show how the value   7.5 3.5 2.5 2.5 6 3 25   is found: row total times column total divided by   15 7 5 5 12 6 50   grand total.>                                     By using either the Excel Chi Square functions or calculating the results directly as the text shows, do we         reject or not reject the null hypothesis?  What does your conclusion mean?           Interpretation:                                                       2 Using our sample data, we can construct a 95% confidence interval for the population’s mean salary for each gender.        Interpret the results.  How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?     Males Mean St error      Low  to  High               52 3.65878     44.4483   59.5517   Results are mean +/-2.064*standard error   Females 38 3.62275     30.5226   45.4774   2.064 is t value for 95% interval   <Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>     Interpretation:                                                                                   3 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?                                         4 Using our sample data, construct a 95% confidence interval for the population’s mean service difference for each gender.         Do they intersect or overlap?  How do these results compare to the findings in week 2, question 2?                                   5 How do you interpret these results in light of our question about equal pay for equal work?